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Calculation: 8192 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × 2 ∴ 8192 should be divided by 2 to make the resulting number a perfect cube. 8192/2 = 4096 4096 is a 16. The correct option is 4 i.e. 2 A perfect cube is a number that is equal to the number, multiplied by itself, three times. India’s #1 Learning Platform Start Complete Exam Preparation
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Mock Tests & Quizzes Trusted by 3.3 Crore+ Students Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now On factorising 8192 into prime factors, we get: \[8192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\] On grouping the factors in triples of equal factors, we get:
\[8192 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 2\] It is evident that the prime factors of 8192 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8192 is not a perfect cube. However, if the number is divided by 2, the factors can be grouped into triples of equal factors such that no factor is left over.Hence, the number 8192 should be divided by 2 to make it a perfect cube. Also, the quotient is given as: \[\frac{8192}{2} = \frac{\left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times 2}{2}\] To get the cube root of the quotient 4096, take one factor from each triple. We get:
Hence, the required numbers are 2 and 16. |